Abstract
Given two strings described by SLPs of total size n, we show how to compute their edit distance in \(\mathcal{O}(nN\sqrt{\log\frac{N}{n}})\) time, where N is the sum of the strings length. The result can be generalized to any rational scoring function, hence we improve the existing \(\mathcal{O}(nN\log N)\) [10] and \(\mathcal{O}(nN\log\frac{N}{n})\) [4] time solutions. This gets us even closer to the \(\mathcal{O}(nN)\) complexity conjectured by Lifshits [7]. The basic tool in our solution is a linear time procedure for computing the max-product of a vector and a unit-Monge matrix, which might be of independent interest.
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References
Andoni, A., Krauthgamer, R., Onak, K.: Polylogarithmic approximation for edit distance and the asymmetric query complexity. In: FOCS, pp. 377–386. IEEE Computer Society (2010)
Charikar, M., Lehman, E., Liu, D., Panigrahy, R., Prabhakaran, M., Sahai, A., Shelat, A.: The smallest grammar problem. IEEE Transactions on Information Theory 51(7), 2554–2576 (2005)
Hermelin, D., Landau, G.M., Landau, S., Weimann, O.: A unified algorithm for accelerating edit-distance computation via text-compression. In: Albers, S., Marion, J.-Y. (eds.) STACS. LIPIcs, vol. 3, pp. 529–540. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany (2009)
Hermelin, D., Landau, G.M., Landau, S., Weimann, O.: Unified compression-based acceleration of edit-distance computation. CoRR, abs/1004.1194 (2010)
Itai, A.: Linear time restricted union/find (2006)
Landau, G.M., Vishkin, U.: Fast parallel and serial approximate string matching. J. Algorithms 10(2), 157–169 (1989)
Lifshits, Y.: Processing Compressed Texts: A Tractability Border. In: Ma, B., Zhang, K. (eds.) CPM 2007. LNCS, vol. 4580, pp. 228–240. Springer, Heidelberg (2007)
Masek, W.J., Paterson, M.: A faster algorithm computing string edit distances. J. Comput. Syst. Sci. 20(1), 18–31 (1980)
Tiskin, A.: Semi-local string comparison: algorithmic techniques and applications. CoRR, abs/0707.3619 (2007)
Tiskin, A.: Fast distance multiplication of unit-Monge matrices. In: Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2010, pp. 1287–1296. Society for Industrial and Applied Mathematics, Philadelphia (2010)
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Gawrychowski, P. (2012). Faster Algorithm for Computing the Edit Distance between SLP-Compressed Strings. In: Calderón-Benavides, L., González-Caro, C., Chávez, E., Ziviani, N. (eds) String Processing and Information Retrieval. SPIRE 2012. Lecture Notes in Computer Science, vol 7608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34109-0_24
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DOI: https://doi.org/10.1007/978-3-642-34109-0_24
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